Import Libraries and Data

Data Structure and Summary Table

## Rows: 159
## Columns: 30
## $ NAME                      <chr> "Rabun", "Towns", "Fannin", "Murray", "Whitf…
## $ FIPS                      <chr> "13241", "13281", "13111", "13213", "13313",…
## $ county                    <chr> "241", "281", "111", "213", "313", "047", "2…
## $ rucc_code13               <fct> non, non, non, sm, sm, mm, non, mm, mm, non,…
## $ rucc_code13_n             <dbl> 6, 6, 6, 4, 4, 3, 6, 3, 3, 6, 5, 6, 6, 5, 5,…
## $ mortality                 <dbl> 4, 3, 5, 6, 15, 10, 2, 13, 4, 6, 10, 8, 7, 7…
## $ population                <dbl> 16602, 11506, 25322, 39782, 104658, 66550, 2…
## $ Year                      <dbl> 2020, 2020, 2020, 2020, 2020, 2020, 2020, 20…
## $ state                     <chr> "13", "13", "13", "13", "13", "13", "13", "1…
## $ pct_poverty               <dbl> 13.6, 8.9, 7.6, 11.8, 11.3, 7.2, 12.1, 10.4,…
## $ vacancy_rate              <dbl> 44.6, 39.6, 36.1, 10.3, 9.5, 8.8, 31.1, 13.6…
## $ unemployment_rate         <dbl> 4.1, 4.2, 5.8, 6.5, 6.0, 3.5, 4.8, 6.8, 5.0,…
## $ unemployment_rate_out     <dbl> 4.1, 4.2, 5.8, 6.5, 6.0, 3.5, 4.8, 6.8, 5.0,…
## $ pct_black                 <dbl> 2.0, 1.8, 0.8, 1.3, 4.5, 3.7, 1.0, 5.2, 2.1,…
## $ dist_to_usroad            <dbl> 177343.881, 229218.710, 177629.928, 65168.05…
## $ dist_to_treatment         <dbl> 100811.3814, 63782.7232, 79264.3957, 4003.75…
## $ incidence                 <dbl> 2.409348e-04, 2.607335e-04, 1.974568e-04, 1.…
## $ mort_rate                 <dbl> 0.24093483, 0.26073353, 0.19745676, 0.150821…
## $ Name                      <chr> "Clayton", "Hiawassee", "Blue Ridge", "Chats…
## $ Name_Seat                 <chr> "Clayton", "Hiawassee", "Blue Ridge", "Chats…
## $ pct_poverty_std           <dbl> -0.15651142, -0.98484701, -1.21396111, -0.47…
## $ vacancy_rate_std          <dbl> 3.08075917, 2.51252486, 2.11476084, -0.81732…
## $ unemployment_rate_std     <dbl> -0.74498218, -0.70715012, -0.10183723, 0.162…
## $ unemployment_rate_out_std <dbl> -0.793303461, -0.751995315, -0.091064977, 0.…
## $ pct_black_std             <dbl> -1.5609990, -1.5723595, -1.6291621, -1.60076…
## $ dist_to_usroad_std        <dbl> 0.92635695, 1.52090721, 0.92963541, -0.35931…
## $ dist_to_treatment_std     <dbl> 1.211776760, 0.425387080, 0.754176404, -0.84…
## $ rucc_code13_4             <fct> mi_non, mi_non, mi_non, mm_sm, mm_sm, mm_sm,…
## $ rucc_code13_5             <fct> mi_non, mi_non, mi_non, sm, sm, mm, mi_non, …
## $ geometry                  <MULTIPOLYGON [US_survey_foot]> MULTIPOLYGON (((88…
Summary Table with rucc_code13_5
Characteristic Overall
N = 159
1
Mortality rate
p-value2
Low
N = 59
1
Moderate
N = 61
1
High
N = 39
1
Rural-Urban Continuum Code



0.008
    Large Central Metro & Large Fringe Metro 29 (18%) 5 (8.5%) 18 (30%) 6 (15%)
    Medium Metro 15 (9.4%) 3 (5.1%) 10 (16%) 2 (5.1%)
    Small Metro 30 (19%) 15 (25%) 8 (13%) 7 (18%)
    Micropolitan & Non-Metro 85 (53%) 36 (61%) 25 (41%) 24 (62%)
Mortality Count 3 (1, 8) 1 (0, 2) 5 (2, 14) 6 (4, 9) <0.001
County Population 22,736 (11,319, 57,089) 21,498 (10,343, 43,014) 27,113 (17,277, 91,600) 20,533 (12,830, 35,871) 0.040
Poverty rate 14.0 (10.1, 18.1) 16.6 (12.7, 20.0) 11.7 (8.7, 16.6) 13.8 (10.0, 17.0) 0.002
Vacancy rate 16 (12, 21) 16 (14, 22) 14 (10, 19) 19 (12, 27) 0.042
Unemployment rate 5.70 (4.30, 7.10) 5.80 (4.20, 8.60) 5.60 (4.70, 6.50) 5.40 (4.20, 6.60) 0.5
Percentage of Black Population 29 (17, 41) 31 (25, 47) 25 (12, 36) 30 (11, 41) 0.012
Distance to interstate 83,373 (21,222, 136,712) 90,371 (47,267, 151,962) 63,821 (10,797, 105,001) 95,523 (39,523, 149,321) 0.035
    Unknown 2 1 1 0
Distance to treatment 19,036 (3,692, 83,602) 14,239 (3,721, 90,642) 21,738 (4,079, 82,826) 16,063 (2,889, 83,596) 0.8
    Unknown 2 1 1 0
1 n (%); Median (Q1, Q3)
2 Fisher’s exact test; Kruskal-Wallis rank sum test

Exploratory Data Analysis

1. NAME

Name of the county

  • There are 159 counties in Georgia.

2 & 3. FIPS code / Code

FIPS code

  • All FIPS codes begin with ‘13’, which represents Georgia’s state code, followed by the specific county codes.

4 & 5. rucc_code13 / rucc_code13_n

Rural-urban continuum code of the County

  • Most counties in Georgia are non-metro, followed by small metro, large fringe metro, micropolitan, and medium metro areas.
    Only Fulton county is classified as a large central metro.
  • Most major metro areas, including large central metro, large fringe metro, and medium metro areas, are concentrated in the northern part of the state, particularly around Atlanta.

6 & 7. mortality / population

8. mort_rate

Mortality rate = mortality count/population in each county

NAME incidence
Turner 0.0010049
Tift 0.0007636
Randolph 0.0005654
Telfair 0.0005629
Wilkinson 0.0005581
  • Located in southern and central Georgia, Turner County has the highest mortality rate at 0.001, followed by Tift (0.0008), Randolph (0.0006), Telfair (0.0006), and Wilkinson (0.0006) counties, which are also in the southern part of the st
  • We aim to identify whether certain covariates in counties are associated with higher or lower mortality rates. On each covariate map, we are looking for emerging patterns across these areas.
The following are summary of the geographic distribution of the covariates that we are interested in.

9. pct_poverty

Percentage of people whose income in the past 12 months is below the poverty level in each county

NAME pct_poverty
Taylor 28.6
Taliaferro 28.5
Terrell 28.0
Jenkins 27.5
Seminole 27.1
  • Taylor County has the highest poverty rate at 28.6%, followed by Taliaferro (28.5%), Terrell (28.0%), Jenkins (27.5%), and Seminole (27.1%) counties.
  • Overall, counties in southern and central Georgia tend to have relatively higher poverty rates compared to those in northern Georgia.

10. vacancy_rate

Percentage of housing vacancy in each county

NAME vacancy_rate
Quitman 53.2
Rabun 44.6
Hancock 43.3
Towns 39.6
Clay 39.2
  • Quitman County has the highest vacancy rate at 53.2%, followed by Rabun (44.6%), Hancock (43.3%), Towns (39.6%), and Clay (39.2%) counties.
  • Vacancy rates vary widely across the state, with high rates observed in northern, central-eastern, and southern Georgia.

11 & 12. unemployment_rate / _out

Unemployment rate (before / after treating outliers) in each county

  • Quitman county has a notably high unemployment rate of 21.4%, making it an outlier among other counties. To address this outlier, we replaced any values above the 99th percentile with the 99th percentile of the ranked value.

NAME unemployment_rate_out
Quitman 13.826
Baker 13.826
Charlton 13.700
Long 12.400
Crisp 12.000
  • After adjusting for outliers, Quitman and Baker counties have the highest unemployment rate at 13.83%, followed by Charlton (13.7%), Long (12.4%), and Crisp (12%) counties.
  • Overall, counties in southern and rural Georgia tend to have higher unemployment rates compared to those in northern Georgia.

13. pct_black

Percentage of county population that is made up of Black people

NAME pct_black
Hancock 72.7
Clayton 72.5
Dougherty 71.2
Randolph 64.4
Macon 62.6
  • Hancock County has the largest percentage of Black population at 72.7%, followed by Clayton (72.5%), Dougherty (71.2%), Randolph (64.4%), and Macon (62.6%) counties.
  • In general, counties with higher percentages of Black populations are more common in central and southwestern Georgia.

14. dist_to_usroad

Distance from County Seat to Interstate

NAME dist_to_usroad
Seminole 446751.5
Miller 388135.0
Early 371694.7
Decatur 364239.2
Bacon 313541.7
  • Seminole County has the longest distance from the county seat to the interstate at 446,752 feet, followed by Miller (338,135 feet), Early (371,695 feet), Decatur (364,239 feet), and Bacon (313,542 feet) counties.
  • Counties in southwestern and southeastern Georgia tend to have longer distances to interstates, particularly in more rural areas.

15. dist_to_treatment

Distance to Treatment Centers

  • U.S. Department of Health and Human Services, Substance Abuse and Mental Health Services Administration, Behavioral Health Services Information System. (2024). FindTreament_Facility_listing. Retrieved from https://findtreatment.gov/locator.
NAME dist_to_treatment
Quitman 185131.5
Warren 164829.7
Stewart 161330.9
Glascock 160496.1
Randolph 153486.9
  • Quitman County has the longest distance to treatment centers at 185,132 feet, followed by Warren (164,830 feet), Stewart (161,331 feet), Glascock (160,496 feet), and Randolph (153,437 feet) counties.
  • Counties in southwestern and rural central Georgia generally have longer distances to treatment centers.

Check the Distribution of Covariates

pct_poverty

vacancy_rate

unemployment_rate_out

pct_black

dist_to_usroad

dist_to_treatment

Poisson Random Intercept Model with a Population Offset


\[ y_i|\mu_i \sim \text{Poisson}(\mu_i), \\ where \ \mu_i = E(y_i) = Var(y_i) \\\ \\ log(\frac{\mu_i}{pop_i}) = \beta_0 + \beta_1\,poverty\_rate_i + \beta_2\,vacancy\_rate_i + \beta_3\,unemployment\_rate_i + \beta_4\,pct\_black_i + \beta_5\,dist\_to\_road_i + \beta_6\,dist\_to\_treatment_i + \theta_i \\\ \\ log(\mu_i) = log\,pop_i + \beta_0 + \beta_1\,poverty\_rate_i + \beta_2\,vacancy\_rate_i + \beta_3\,unemployment\_rate_i + \beta_4\,pct\_black_i + \beta_5\,dist\_to\_road_i + \beta_6\,dist\_to\_treatment_i + \theta_i \\\ \\ \theta_i \sim N(0,\tau^2) \]

  • \(y_i\) : mortality count for county i

  • \(\mu_i\) : expected mortality count for county i

  • \(log\,pop_i\) : population of county i, used as an offset to adjust for the different population sizes across the counties

  • \(\beta_0\) : baseline log expected mortality rate

  • \(\theta_i\) : random intercept for county i, county-specific deviation in baseline log expected mortality rate

  • \(e^{\beta_1}\) : relative mortality rate change for a one standard deviation increase in the poverty rate

  • \(e^{\beta_2}\) : relative mortality rate change for a one standard deviation increase in the vacancy rate

  • \(e^{\beta_3}\) : relative mortality rate change for a one standard deviation increase in the unemployment rate

  • \(e^{\beta_4}\) : relative mortality rate change for a one standard deviation increase in the percentage of black population

  • \(e^{\beta_5}\) : relative mortality rate change for a one standard deviation increase in the distance to the interstate

  • \(e^{\beta_6}\) : relative mortality rate change for a one standard deviation increase in the distance to the treatment center

Fit the Model

# Fit the poisson regression model
dat$log_pop = log(dat$population)
fit = glmer(mortality ~ offset(log_pop) + pct_poverty_std + vacancy_rate_std +
              unemployment_rate_out_std + pct_black_std + dist_to_usroad_std + 
              dist_to_treatment_std + (1|county),
            family = poisson(link = "log"), data = dat)
summary(fit)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: mortality ~ offset(log_pop) + pct_poverty_std + vacancy_rate_std +  
##     unemployment_rate_out_std + pct_black_std + dist_to_usroad_std +  
##     dist_to_treatment_std + (1 | county)
##    Data: dat
## 
##      AIC      BIC   logLik deviance df.resid 
##    753.0    777.5   -368.5    737.0      149 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.34923 -0.54256 -0.04798  0.37666  2.74739 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  county (Intercept) 0.1948   0.4413  
## Number of obs: 157, groups:  county, 157
## 
## Fixed effects:
##                           Estimate Std. Error  z value Pr(>|z|)    
## (Intercept)               -8.93104    0.06266 -142.541   <2e-16 ***
## pct_poverty_std            0.01450    0.07978    0.182   0.8558    
## vacancy_rate_std           0.15993    0.07527    2.125   0.0336 *  
## unemployment_rate_out_std -0.13974    0.07645   -1.828   0.0676 .  
## pct_black_std             -0.07285    0.06573   -1.108   0.2677    
## dist_to_usroad_std        -0.17990    0.07779   -2.313   0.0207 *  
## dist_to_treatment_std      0.03392    0.07356    0.461   0.6447    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) pct_p_ vcnc__ unm___ pct_b_ dst_t_s_
## pct_pvrty_s  0.087                                     
## vcncy_rt_st  0.026 -0.320                              
## unmplymn___  0.086 -0.189  0.126                       
## pct_blck_st -0.016 -0.402  0.045 -0.343                
## dst_t_srd_s  0.181 -0.247 -0.315 -0.004  0.183         
## dst_t_trtm_  0.200 -0.066 -0.356 -0.080  0.047  0.004
  • The baseline relative mortality rate is \(e^\hat{\beta_0}\) = \(e^{-8.93}\) = 0.0001.

  • There exists heterogeneity in baseline mortality rate with a between-county standard deviation \(\tau\) of 0.44.
    So 95% of the counties have baseline mortality rates between \(e^{-8.93 \pm 1.96 \times 0.44}\) = (0.00006, 0.0003).

  • There is evidence that mortality rate increases by approximately 17.4% (\(e^\hat{\beta_2}\) = \(e^{0.16}\) = 1.174) for a one standard deviation increase in the vacancy rate.

  • There is evidence that mortality rate decreases by approximately 16.5% (\(e^\hat{\beta_5}\) = \(e^{-0.180}\) = 0.835) for a one standard deviation increase in the distance to the interstate.